The present invention relates to a traction sheave elevator consisting of a drive machine and a traction sheave coupled with it, said traction sheave being provided with a rope groove, the hoisting rope running over the traction sheave, an elevator car and its counterweight, the elevator car being suspended on the hoisting rope and moving in an elevator shaft, said elevator using at least one diverting pulley so as to cause the hoisting rope going to the traction sheave and the hoisting rope coming from the traction sheave to run crossways.